Question

1999^2-1998^2+1997^2-...-2^2+1^2​

Answer 1

675 (6913)

`/`

`+`

Answer 2

Answer:1999000

Explanation:

1²-2²=(1-2)(1+2)=-1*3=-3

3²-4²=(3-4)(3+4)=-7

5²-6²=(5-6)(5+6)=-11

7²-8²=(7-8)(7+8)=-15

...

1997²-1998²=(1997-1998)(1997+1998)=-3995

1²-2²+3²-4²+....+1997²-1998²+1999²=1999²-(3+7+11+15+...+3995)

Number of terms in the parenthesis: =(3995-3)/(7-3)+1=998+1=999

Parenthesis=

`((3995+3)*999)/(2) =(3998*999)/(2) =1997001`

1²-2²+3²-4²+....+1997²-1998²+1999²==1999²-1997001=1999000